Package 'spatialkernel' reference manual

Title:	Non-Parametric Estimation of Spatial Segregation in a Multivariate Point Process
Description:	Edge-corrected kernel density estimation and binary kernel regression estimation for multivariate spatial point process data. For details, see Diggle, P.J., Zheng, P. and Durr, P. A. (2005) <doi:10.1111/j.1467-9876.2005.05373.x>.
Authors:	Virgilio Gómez-Rubio [aut, cre], Pingping Zheng [aut], Peter Diggle [aut, cph], Richard Cotton [ctb], Alan Murta [ctb, cph], Jonathan Richard Shewchuk [ctb, cph], Barry Rowlingson [ctb, cph], Wm. Randolph Franklin [ctb, cph], David C. Sterratt [cph, aut], Elias Pipping [ctb], Roger D. Peng [aut], Duncan Murdoch [aut], Barry Rowlingson [aut]
Maintainer:	Virgilio Gómez-Rubio <[email protected]>
License:	CC BY-NC-SA 4.0
Version:	0.4-25
Built:	2024-11-06 03:56:12 UTC
Source:	https://github.com/barryrowlingson/spatialkernel

The Spatialkernel Package

Description

An R package for spatial point process analysis.

Details

This package contains functions for spatial point process analysis using kernel smoothing methods. This package has been written to be compatible with the splancs package which is available on CRAN (The Comprehensive R Archive Network).

For a complete list of functions with individual help pages, use library(help = \ "spatialkernel").

Maintainer

Pingping Zheng [email protected]

Note

For the convience of the user, we present here examples which show how to use some of the functions in the package.

Author(s)

Pingping Zheng and Peter Diggle

References

P. Zheng, P.A. Durr and P.J. Diggle (2004) Edge-correction for Spatial Kernel Smoothing — When Is It Necessary? Proceedings of the GisVet Conference 2004, University of Guelph, Ontario, Canada, June 2004.
Diggle, P.J., Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. J. R. Stat. Soc. C, 54, 3, 645–658.

Examples

## An example of spatial segregation analysis
## Not run: 
  ## source in Lansing Woods tree data within a polygon boundary
  data(lansing)
  data(polyb)
  ## select data points within polygon
  ndx <- which(pinpoly(polyb, as.matrix(lansing[c("x", "y")])) > 0)
  pts <- as.matrix(lansing[c("x", "y")])[ndx,]
  marks <- lansing[["marks"]][ndx]
  ## select bandwidth
  h <- seq(0.02, 0.1, length=101)
  cv <- cvloglk(pts, marks, h=h)$cv
  hcv <- h[which.max(cv)]
  plot(h, cv, type="l")
  ## estimate type-specific probabilities and do segregation tests
  ## by one integrated function
  sp <- spseg(pts, marks, hcv, opt=3, ntest=99, poly=polyb)
  ## plot estimated type-specific probability surfaces
  plotphat(sp)
  ## additional with pointwise significance contour lines
  plotmc(sp, quan=c(0.025, 0.975))
  ## p-value of the Monte Carlo segregation test
  cat("\np-value of the Monte Carlo segregation test", sp$pvalue)
  
  ##estimate intensity function at grid point for presentation
  ##with bandwidth hcv
  gridxy <- as.matrix(expand.grid(x=seq(0, 1, length=101), y=seq(0, 1, length=101)))
  ndx <- which(pinpoly(polyb, gridxy) > 0) ##inside point index
  lam <- matrix(NA, ncol=101, nrow=101)
  lam[ndx] <- lambdahat(pts, hcv, gpts = gridxy[ndx,], poly =
      polyb)$lambda
  brks <- pretty(range(lam, na.rm=TRUE), n=12)
  plot(0, 0, xlim=0:1, ylim=0:1, xlab="x", ylab="y", type="n")
  image(x=seq(0, 1, length=101), y=seq(0, 1, length=101),
    z=lam, add=TRUE, breaks=brks, col=risk.colors(length(brks)-1))
  polygon(polyb)
  metre(0, 0.01, 0.05, 0.51, lab=brks, col=risk.colors(length(brks)-1), cex=1)
  
  ## An example of inhomogeneous intensity function and K function
  ## estimated with the same data
  s <- seq(0, 0.06, length=101)
  lam <- lambdahat(pts, hcv, poly=polyb)$lambda
  kin <- kinhat(pts, lam, polyb, s)
  plot(kin$s, kin$k-pi*(kin$s)^2, xlab="s", ylab="k-pi*s^2", type="l")

## End(Not run)
## An example of spatial segregation analysis
## Not run: 
  ## source in Lansing Woods tree data within a polygon boundary
  data(lansing)
  data(polyb)
  ## select data points within polygon
  ndx <- which(pinpoly(polyb, as.matrix(lansing[c("x", "y")])) > 0)
  pts <- as.matrix(lansing[c("x", "y")])[ndx,]
  marks <- lansing[["marks"]][ndx]
  ## select bandwidth
  h <- seq(0.02, 0.1, length=101)
  cv <- cvloglk(pts, marks, h=h)$cv
  hcv <- h[which.max(cv)]
  plot(h, cv, type="l")
  ## estimate type-specific probabilities and do segregation tests
  ## by one integrated function
  sp <- spseg(pts, marks, hcv, opt=3, ntest=99, poly=polyb)
  ## plot estimated type-specific probability surfaces
  plotphat(sp)
  ## additional with pointwise significance contour lines
  plotmc(sp, quan=c(0.025, 0.975))
  ## p-value of the Monte Carlo segregation test
  cat("\np-value of the Monte Carlo segregation test", sp$pvalue)
  
  ##estimate intensity function at grid point for presentation
  ##with bandwidth hcv
  gridxy <- as.matrix(expand.grid(x=seq(0, 1, length=101), y=seq(0, 1, length=101)))
  ndx <- which(pinpoly(polyb, gridxy) > 0) ##inside point index
  lam <- matrix(NA, ncol=101, nrow=101)
  lam[ndx] <- lambdahat(pts, hcv, gpts = gridxy[ndx,], poly =
      polyb)$lambda
  brks <- pretty(range(lam, na.rm=TRUE), n=12)
  plot(0, 0, xlim=0:1, ylim=0:1, xlab="x", ylab="y", type="n")
  image(x=seq(0, 1, length=101), y=seq(0, 1, length=101),
    z=lam, add=TRUE, breaks=brks, col=risk.colors(length(brks)-1))
  polygon(polyb)
  metre(0, 0.01, 0.05, 0.51, lab=brks, col=risk.colors(length(brks)-1), cex=1)
  
  ## An example of inhomogeneous intensity function and K function
  ## estimated with the same data
  s <- seq(0, 0.06, length=101)
  lam <- lambdahat(pts, hcv, poly=polyb)$lambda
  kin <- kinhat(pts, lam, polyb, s)
  plot(kin$s, kin$k-pi*(kin$s)^2, xlab="s", ylab="k-pi*s^2", type="l")

## End(Not run)

Signed Area of Polygon

Description

Calculate the area of a polygon and its boundary direction.

Usage

areapoly(poly)
areapoly(poly)

Arguments

poly

matrix containing the x,y-coordinates of the vertices of the polygon boundary.

Value

area: positive numeric, the area of the polygon.
sign: integer, 1 if the polygon orientation is anticlockwise, -1 otherwise.
poly: copy of the passed argument poly.

Note

This function is provided here so that users do not need to load other packages, as it is not available in the base R packages.

References

Joseph O'Rourke, Computational Geometry in C (2nd Edition), Cambridge University Press, 2000 edition.

Cross-Validated Log-Likelihood Function Calculate the cross-validated log-likelihood function.

Description

Select a common bandwidth for kernel regression estimation of type-specific probabilities of a multivariate Poisson point process with independent component processes of each categorical type by maximizing the cross-validate log-likelihood function.

Usage

cvloglk(pts, marks, t = NULL, h)
cvloglk(pts, marks, t = NULL, h)

Arguments

`pts`	matrix containing the `x,y`-coordinates of the point locations.
`marks`	numeric/character vector of the marked labels of the type of each point.
`t`	numeric vector of the associated time-periods, default `NULL` for pure spatial data.
`h`	numeric vector of the kernel smoothing bandwidths at which to calculate the cross-validated log-likelihood function.

Details

Select a common bandwidth for kernel regression of type-specific probabilities for all time-periods when the argument t is not NULL, in which case the data is of a multivariate spatial-temporal point process, with t the values of associated time-periods.

Value

A list with components

cv: vector of the values of the cross-validated Log-likelihood function.
hcv: numeric value which maximizing the cross-validate log-likelihood function
...: copy of the arguments pts, marks, h.

References

Diggle, P.J., Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. J. R. Stat. Soc. C, 54, 3, 645–658.

Lansing Woods Trees

Description

This is the Lansing Woods Tree data set and an arbitrary polygon boundary within unit square.

Format

lansing is an R data.frame with x, y, marks and polyb is an R matrix with x, y.

Note

The Lansing Woods tree data set and the arbitrary polygon are provided here for the demonstration of the basic usage of this package. See Section Examples in spatialkernel-package.

Source

Lansing Woods trees from Lansing Woods, Clinton County, Michigan USA, including hickories, maples, and oaks.

References

Gerrard, D.J. (1969) Competition quotient: a new measure of the competition affecting individual forest trees. Research Bulletin 20, Agricultural Experiment Station, Michigan State University.

Level (Contour) Plots with Polygonal Boundary This is a revised version of the base R function `filled.contour`. It additionally plots a polygonal boundary.

Description

Level (Contour) Plots with Polygonal Boundary This is a revised version of the base R function filled.contour. It additionally plots a polygonal boundary.

Usage

filled.contour.poly(
  x = seq(min(poly[, 1]), max(poly[, 1]), len = nrow(z)),
  y = seq(min(poly[, 2]), max(poly[, 2]), len = ncol(z)),
  z,
  poly,
  xlim = range(x, finite = TRUE),
  ylim = range(y, finite = TRUE),
  zlim = range(z, finite = TRUE),
  levels = pretty(zlim, nlevels),
  nlevels = 10,
  color.palette = risk.colors,
  col = color.palette(length(levels) - 1),
  llevels = levels,
  labels = NULL,
  labcex = 0.6,
  drawlabel = TRUE,
  method = "flattest",
  vfont = c("sans serif", "plain"),
  lcol = par("fg"),
  lty = par("lty"),
  lwd = par("lwd"),
  plot.title,
  plot.axes,
  key.title,
  key.axes,
  asp = NA,
  xaxs = "i",
  yaxs = "i",
  las = 1,
  axes = TRUE,
  ...
)
filled.contour.poly(
  x = seq(min(poly[, 1]), max(poly[, 1]), len = nrow(z)),
  y = seq(min(poly[, 2]), max(poly[, 2]), len = ncol(z)),
  z,
  poly,
  xlim = range(x, finite = TRUE),
  ylim = range(y, finite = TRUE),
  zlim = range(z, finite = TRUE),
  levels = pretty(zlim, nlevels),
  nlevels = 10,
  color.palette = risk.colors,
  col = color.palette(length(levels) - 1),
  llevels = levels,
  labels = NULL,
  labcex = 0.6,
  drawlabel = TRUE,
  method = "flattest",
  vfont = c("sans serif", "plain"),
  lcol = par("fg"),
  lty = par("lty"),
  lwd = par("lwd"),
  plot.title,
  plot.axes,
  key.title,
  key.axes,
  asp = NA,
  xaxs = "i",
  yaxs = "i",
  las = 1,
  axes = TRUE,
  ...
)

Arguments

`x`	locations of grid lines at which the values in `z` are measured. These must be in ascending order. By default, equally spaced values from 0 to 1 are used. If `x` is a list, its components `x$x` and `x$y` are used for `x` and `y`, respectively. If the list has component `z` this is used for `z`.
`y`	See `x` arg.
`z`	a matrix containing the values to be plotted (`NA`s are allowed). Note that `x` can be used instead of `z` for convenience.
`poly`	a matrix containing the `x,y`-coordinates of the vertices of the polygon boundary.
`xlim`	`x` limits for the plot.
`ylim`	`y` limits for the plot.
`zlim`	`z` limits for the plot.
`levels`	a set of levels which are used to partition the range of `z`. Must be strictly increasing (and finite). Areas with `z` values between consecutive levels are painted with the same color.
`nlevels`	if `levels` is not specified, the range of `z` is divided into approximately this many levels.
`color.palette`	a color palette function used to assign colors in the plot.
`col`	an explicit set of colors to be used in the plot. This argument overrides any palette function specification.
`llevels`	numeric vector of levels at which to draw contour lines, default is the same as `levels`.
`labels`	a vector giving the labels for the contour lines. If `NULL` then the levels are used as labels.
`labcex`	`cex` for contour labelling.
`drawlabel`	logical, contour lines are labelled if `TRUE`.
`method`	character string specifying where the labels will be located. Possible values are "simple", "edge" and "flattest" (the default). See the Details section.
`vfont`	if a character vector of length 2 is specified, then Hershey vector fonts are used for the contour labels. The first element of the vector selects a typeface and the second element selects a fontindex (see `text` for more information).
`lcol`	color for the lines drawn.
`lty`	line type for the lines drawn.
`lwd`	line width for the lines drawn.
`plot.title`	statement which add title to the main plot.
`plot.axes`	statement which draws axes on the main plot. This overrides the default axes.
`key.title`	statement which adds title to the plot key.
`key.axes`	statement which draws axes on the plot key. This overrides the default axis.
`asp`	the `y/x` aspect ratio, see `plot.window`.
`xaxs`	the `x` axis style. The default is to use internal labeling.
`yaxs`	the `y` axis style. The default is to use internal labeling.
`las`	the style of labeling to be used. The default is to use horizontal labeling.
`axes`	Logical. Should axes be drawn? See `plot.default`.
`...`	additional graphical parameters.

Note

By defining z values as NA at points outside the polygonal boundary, filled.contour.poly produces a contour plot within the polygonal boundary.

Inhomogeneous K-function Estimation Estimate the inhomogeneous K function of a non-stationary point pattern.

Description

Inhomogeneous K-function Estimation Estimate the inhomogeneous K function of a non-stationary point pattern.

Usage

kinhat(pts, lambda, poly, s)
kinhat(pts, lambda, poly, s)

Arguments

`pts`	matrix of the `x,y`-coordinates of the point locations.
`lambda`	intensity function evaluated at the above point locations.
`poly`	matrix of the `x,y`-coordinates of the polygon boundary.
`s`	vector of distances at which to calculate the K function.

Details

The inhomogeneous K function is a generalization of the usual K function defined for a second-order intensity-reweighted stationary point process, proposed by Baddeley et\ al (2000).

When the true intensity function is unknown, and is to be estimated from the same data as been used to estimate the K function, a modified kernel density estimation implemented in lambdahat with argument gpts=NULL can be used to calculate the estimated intensity at data points. See Baddeley et al (2000) for details, and Diggle, P.J., et al (2006) for a cautious note.

Value

A list with components

k: values of estimated K at the distances s.
s: copy of s.

Note

This code is adapted from splancs (Rowlingson and Diggle, 1993) fortran code for the estimation of homogeneous K function khat, with edge correction inherited for a general polygonal area.

References

Baddeley, A. J. and M?ller, J. and Waagepetersen R. (2000) Non and semi-parametric estimation of interaction in inhomogeneous point patterns, Statistica Neerlandica, 54, 3, 329–350.
Diggle, P.J., V. G $\acute{\mathrm{o}}$ mez-Rubio, P.E. Brown, A.G. Chetwynd and S. Gooding (2006) Second-order analysis of inhomogeneous spatial point processes using case-control data, submitted to Biometrics.
Rowlingson, B. and Diggle, P. (1993) Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627–655.

Kernel Density Estimation of Intensity Function

Description

Kernel density estimation of the intensity function of a two-dimensional point process.

Usage

lambdahat(pts, h, gpts = NULL, poly = NULL, edge = TRUE)
lambdahat(pts, h, gpts = NULL, poly = NULL, edge = TRUE)

Arguments

`pts`	matrix containing the `x,y`-coordinates of the data point locations.
`h`	numeric value of the bandwidth used in the kernel smoothing.
`gpts`	matrix containing the `x,y`-coordinates of point locations at which to calculate the intensity function, usually a fine grid points within `poly`, default `NULL` to estimate intensity function at data locations.
`poly`	matrix containing the `x,y`-coordinates of the vertices of the polygon boundary in an anticlockwise order.
`edge`	logical, with default `TRUE` to do edge-correction.

Details

Kernel smoothing methods are widely used to estimate the intensity of a spatial point process. One problem which arises is the need to handle edge effects. Several methods of edge-correction have been proposed. The adjustment factor proposed in Berman and Diggle (1989) is a double integration $\int_AK[(x-x_0)/h]/h^2$ , where $A$ is a polygonal area, $K$ is the smoothing kernel and $h$ is the bandwidth used for the smoothing. Zheng, P. et\ al (2004) proposed an algorithm for fast calculate of Berman and Diggle's adjustment factor.

When gpts is NULL, lambdahat uses a leave-one-out estimator for the intensity at each of the data points, as been suggested in Baddeley et al (2000). This leave-one-out estimate at each of the data points then can be used in the inhomogeneous K function estimation kinhat when the true intensity function is unknown.

The default kernel is the Gaussian. The kernel function is selected by calling setkernel.

Value

A list with components

lambda: numeric vector of the estimated intensity function.
...: copy of the arguments pts, gpts, h, poly, edge.

Note

In principle, the double adaptive double integration algorithm of Zheng, P. et\ al (2004) can be applied to other kernel functions. Furthermore, the area at the present is enclosed by a simple polygon which could be generalized into a complex area with polygonal holes inside. For instance, a large lake lays within the land area of study.

Other source codes used in the implementation of the double integration algorithm include

Laurie, D.P. (1982) adaptive cubature code in Fortran;
Shewchuk, J.R. triangulation code in C;
Alan Murta's polygon intersection code in C (Project: Generic Polygon Clipper).

References

M. Berman and P. Diggle (1989) Estimating weighted integrals of the second-order intensity of a spatial point process, J. R. Stat. Soc. B, 51, 81–92.
P. Zheng, P.A. Durr and P.J. Diggle (2004) Edge–correction for Spatial Kernel Smoothing — When Is It Necessary? Proceedings of the GisVet Conference 2004, University of Guelph, Ontario, Canada, June 2004.
Baddeley, A. J. and Møller, J. and Waagepetersen R. (2000) Non and semi-parametric estimation of interaction in inhomogeneous point patterns, Statistica Neerlandica, 54, 3, 329–350.
Laurie, D.P. (1982). Algorithm 584 CUBTRI: Adaptive Cubature over a Triangle. ACM–Trans. Math. Software, 8, 210–218.
Jonathan R. Shewchuk, Triangle, a Two-Dimensional Quality Mesh Generator and Delaunay Triangulator at http://www-2.cs.cmu.edu/~quake/triangle.html.
Alan Murta, General Polygon Clipper at http://www.cs.man.ac.uk/~toby/gpc.
NAG's Numerical Library. Chapter 11: Quadrature, NAG's Fortran 90 Library. https://www.nag.co.uk/numeric/fn/manual/html/c11_fn04.html

Monte Carlo Inference of Temporal Changes in Spatial Segregation An approximate Monte Carlo test of temporal changes in a multivariate spatial-temporal point process.

Description

Monte Carlo Inference of Temporal Changes in Spatial Segregation An approximate Monte Carlo test of temporal changes in a multivariate spatial-temporal point process.

Usage

mcpat.test(pts, marks, t, h, ntest = 100, proc = TRUE)
mcpat.test(pts, marks, t, h, ntest = 100, proc = TRUE)

Arguments

`pts`	matrix containing the `x,y`-coordinates of the data point locations.
`marks`	numeric/character vector of the marked type labels of the data points.
`t`	numeric vector of the associated time-periods.
`h`	numeric vector of the bandwidths at which to calculate the cross-validated log-likelihood function pooled over times.
`ntest`	integer with default 100, number of simulations for the Monte Carlo test
`proc`	logical, default `TRUE` prints the processing messages.

Details

The spatial-temporal data are denoted as $(x_i, m_i, t_i)$ , where $x_i$ are the spatial locations, $m_i$ are the categorical mark sequence numbers, and $t_i$ are the associated time-periods.

The null hypothesis is that the type-specific probability surfaces are constant over time-periods, i.e., $p_k(x, t)=p_k(x)$ , for any $t$ , where $p_k(x, t)$ are the type-specific probabilities for $k$ th category within time-period $t$ .

Each Monte Carlo simulation is sampled from an approximate true type-specific probability surfaces — the estimated one from the data. Approximately, the simulated data and the original data are samples from the same probability distribution under the null hypothesis. See Diggle, P.J. et al (2005) for more details.

Value

A list with components

pvalue: $p$ -value of the approximate Monte Carlo test.
...: copy of pts, marks, t, h, ntest.

References

Diggle, P. J. and Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. J. R. Stat. Soc. C, 54, 3, 645–658.

Monte Carlo Test of Spatial Segregation in Multivariate Point Process

Description

Monte Carlo test of spatial segregation in a multivariate point process by simulating data from random re-labelling of the categorical marks.

Usage

mcseg.test(pts, marks, h, stpts = NULL, ntest = 100, proc = TRUE)
mcseg.test(pts, marks, h, stpts = NULL, ntest = 100, proc = TRUE)

Arguments

`pts`	matrix containing the `x,y`-coordinates of the data point locations.
`marks`	numeric/character vector of the marked type labels of the point pattern.
`h`	numeric vector of the bandwidths at which to calculate the cross-validated likelihood function.
`stpts`	matrix containing the `x,y`-coordinates of the locations at which to implement the pointwise segregation test, with default `NULL` not to do the pointwise segregation test.
`ntest`	integer with default 100, number of simulations for the Monte Carlo test.
`proc`	logical with default `TRUE` to print the processing messages.

Details

The null hypothesis is that the estimated risk surface is spatially constant, i.e., the type-specific probabilities are $p_k(x)=p_k$ , for all $k$ , see phat. Each Monte Carlo simulation is done by relabeling the data categorical marks at random whilst preserving the observed number of cases of each type.

The segregation test can also be done pointwise, usually at a fine grid of points, to mark the areas where the estimated type-specific probabilities are significantly greater or smaller than the spatial average.

Value

A list with components

pvalue: numeric, $p$ -value of the Monte Carlo test.
stpvalue: matrix, $p$ -values of the test at each point in stpts (if stpts is not NULL), with each column corresponds to one type
...: copy of the arguments pts, marks, h, stpts, ntest, proc.

References

Kelsall, J. E. and Diggle, P. J. (1998) Spatial variation in risk: a nonparametric binary regression approach, Applied Statistics, 47, 559–573.
Diggle, P. J. and Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. J. R. Stat. Soc. C, 54, 3, 645–658.

Plot Color Level Metre

Description

This is a simple function provided here for the convenience of users. It adds a key showing how the colors map to the values of an image plot.

Usage

metre(
  xl,
  yb,
  xr,
  yt,
  lab,
  cols = risk.colors(length(lab) - 1),
  shift = 0,
  cex = 1
)
metre(
  xl,
  yb,
  xr,
  yt,
  lab,
  cols = risk.colors(length(lab) - 1),
  shift = 0,
  cex = 1
)

Arguments

`xl`	Left coordinate of the color level metre bar.
`yb`	Bottom coordinate of the color level metre bar.
`xr`	Right coordinate of the color level metre bar.
`yt`	Top coordinate of the color level metre bar.
`lab`	metre level labels in the metre.
`cols`	associated colours, defaults to use `risk.colors`.
`shift`	distance to shift the label texts away from the metre bar.
`cex`	numeric character expansion factor.

Listing Loaded/Installed Package Versions List version numbers of loaded or installed packages.

Description

Listing Loaded/Installed Package Versions List version numbers of loaded or installed packages.

Usage

package.version(all.available = FALSE, lib.loc = NULL)
package.version(all.available = FALSE, lib.loc = NULL)

Arguments

`all.available`	logical, if `TRUE` return all available packages.
`lib.loc`	character vector describing the location of R library trees to search through, or `NULL`. The default value of `NULL` corresponds to all libraries currently known.

Details

This is a revised version of the base R function .package. It gives both package names and their version numbers.

Value

A list with components

package: names of loaded or available packages if all.available is TRUE.
version: associated package versions.

Estimate Type-Specific Probabilities

Description

Estimate the type-specific probabilities for a multivariate Poisson point process with independent component processes of each type.

Usage

phat(gpts, pts, marks, h)
phat(gpts, pts, marks, h)

Arguments

`gpts`	matrix containing the `x,y`-coordinates of the point locations at which type-specific probabilities are estimated.
`pts`	matrix containing the `x,y`-coordinates of the data points.
`marks`	numeric/character vector of the types of the point in the data.
`h`	numeric value of the bandwidth used in the kernel regression.

Details

The type-specific probabilities for data $(x_i, m_i)$ , where $x_i$ are the spatial point locations and $m_i$ are the categorical mark sequence numbers, $m_i=1,2,\ldots$ , are estimated using the kernel smoothing methodology $\hat p_k(x)=\sum_{i=1}^nw_{ik}(x)I(m_i=k)$ , where $w_{ik}(x)=w_k(x-x_i)/\sum_{j=1}^n w_k(x-x_j)$ , $w_k(.)$ is the kernel function with bandwidth $h_k>0$ , $w_k(x)=w_0(x/h_k)/h_k^2$ , and $w_0(\cdot)$ is the standardised form of the kernel function.

The default kernel is the Gaussian. Different kernels can be selected by calling setkernel.

Value

A list with components

p: matrix of the type-specific probabilities for all types, with the type marks as the matrix row names.
...: copy of the arguments pts, dpts, marks, h.

References

Diggle, P. J. and Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. J. R. Stat. Soc. C, 54, 3, 645–658.

Check if Points are within Polygon

Description

Check the location of point(s) with respect to a polygon.

Usage

pinpoly(poly, pts)
pinpoly(poly, pts)

Arguments

`poly`	matrix containing the `x,y`-coordinates of the vertices of the polygon boundary.
`pts`	matrix of containing the `x,y`-coordinates of the point locations.

Value

An integer vector of indicators for each point in pts,

-1: error when number of polygon vertices exceeds 3000;
0: outside the polygon;
1: at the polygon boundary;
2: inside the polygon.

Note

This function is provided here so that users do not need to load other packages, as it is not available in the base R packages. THE VERTICES MAY BE LISTED CLOCKWISE OR ANTICLOCKWISE

The return values have been changed from the original ones so that the point is inside (including at the boundary) if positive.

References

This Fortran code comes from Wm Randolph Franklin, Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, New York, at website https://wrf.ecse.rpi.edu/nikola/pages/.

Color Palette

Description

This color palette is designed to show risk levels with different colours from small risk (bright orange) to high risk (dark red).

Usage

risk.colors(n)
risk.colors(n)

Arguments

`n`	number of colors (>= 1) to be in the palette.

Examples

  ## risk pie with ten levels
  pie(rep(1,10), labels = seq(0.1, 1, 0.1), col = risk.colors(10))
## risk pie with ten levels
  pie(rep(1,10), labels = seq(0.1, 1, 0.1), col = risk.colors(10))

Select Smoothing Kernel Function

Description

Select a kernel function for kernel regression and kernel smoothing.

Usage

setkernel(kernel = NULL)
setkernel(kernel = NULL)

Arguments

kernel

character string giving the smoothing kernel to be used. This must be one of gaussian, epanechnikov, quadratic, quartic, or NULL, and may be abbreviated to a unique prefix.

Value

A character string of the kernel function selected, or the kernel function currently being used when kernel is NULL.

Note

The default kernel used is Gaussian. Unless users want to use a non-default kernel, there is no need to call setkernel. quadratic is an alias for epanechnikov.

setkernel setup kernel function for both kernel regression in the type-specific probability estimation and the kernel smoothing in the intensity function estimation.

Examples

## Not run: 
  setkernel("e") ## Select "epanechnikov" kernel
  setkernel()    ## show the kernel currrently being used

## End(Not run)
## Not run: 
  setkernel("e") ## Select "epanechnikov" kernel
  setkernel()    ## show the kernel currrently being used

## End(Not run)

Integrated Functions for Spatial Segregation Analysis Spatial segregation analysis to be performed by a single function and presentations by associated `plot` functions.

Description

Run the spatial segregation analysis

spseg for spatstat objects

Usage

## S3 method for class 'matrix'
spseg(
  pts,
  marks,
  h,
  opt = 2,
  ntest = 100,
  poly = NULL,
  delta = min(apply(apply(pts, 2, range), 2, diff))/100,
  proc = TRUE,
  ...
)

plotcv(obj, ...)

plotphat(
  obj,
  types = unique(obj$marks),
  sup = TRUE,
  col = risk.colors(10),
  breaks = seq(0, 1, length = length(col) + 1),
  ...
)

plotmc(
  obj,
  types = unique(obj$marks),
  quan = c(0.05, 0.95),
  sup = FALSE,
  col = risk.colors(10),
  breaks = seq(0, 1, length = length(col) + 1),
  ...
)

spseg(pts, ...)

## S3 method for class 'ppp'
spseg(pts, h, opt, ...)
## S3 method for class 'matrix'
spseg(
  pts,
  marks,
  h,
  opt = 2,
  ntest = 100,
  poly = NULL,
  delta = min(apply(apply(pts, 2, range), 2, diff))/100,
  proc = TRUE,
  ...
)

plotcv(obj, ...)

plotphat(
  obj,
  types = unique(obj$marks),
  sup = TRUE,
  col = risk.colors(10),
  breaks = seq(0, 1, length = length(col) + 1),
  ...
)

plotmc(
  obj,
  types = unique(obj$marks),
  quan = c(0.05, 0.95),
  sup = FALSE,
  col = risk.colors(10),
  breaks = seq(0, 1, length = length(col) + 1),
  ...
)

spseg(pts, ...)

## S3 method for class 'ppp'
spseg(pts, h, opt, ...)

Arguments

`pts`	an object that contains the points. This could be a two-column matrix or a ppp object from spatstat.
`marks`	numeric/character vector of the types of the point in the data.
`h`	numeric vector of the kernel smoothing bandwidth at which to calculate the cross-validated log-likelihood function.
`opt`	integer, 1 to select bandwidth; 2 to calculate type-specific probabilities; and 3 to do the Monte Carlo segregation test.
`ntest`	integer with default 100, number of simulations for the Monte Carlo test.
`poly`	matrix containing the `x,y`-coordinates of the polygonal boundary of the data.
`delta`	spacing distance of grid points at which to calculate the estimated type-specific probabilities for `image` plot.
`proc`	logical with default `TRUE` to print the processing message.
`...`	other arguments concerning `plot` and `points`
`obj`	list of the returning value of `spseg`.
`types`	numeric/character types of the marks of data points to plot the estimated type-specific probabilities, default to plot all types.
`sup`	logical with default `FALSE`, if `TRUE` to superimpose data points on the estimated type-specific probability surface.
`col`	list of colors such as that generated by `risk.colors`.
`breaks`	a set of breakpoints for the `col`: must give one more breakpoint than colour.
`quan`	numeric, the pointwise significance levels to add contours to `image` plot of the estimated type-specific probability surface, with default of `c(0.05, 0.95)`.

Details

spseg implements a complete spatial segregation analysis by selecting bandwidth, calculating the type-specific probabilities, and then carrying out the Monte Carlo test of spatial segregation and pointwise significance. Some plot functions are also provided here so that users can easily present the results.

These functions are provided only for the convenience of users. Users can instead use individual functions to implement the analysis step by step and plot the diagrams as they wish.

Examples of how to use spseg and present results using plot functions are presented in spatialkernel-package.

This is the details of the S3 generic method

Does spseg for marked ppp objects

Value

A list with components

hcv: bandwidth selected by the cross-validated log-likelihood function.
gridx,gridy: x, y coordinate vectors at which the grid points are generated at which to calculate the type-specific probabilities and pointwise segregation test p-value.
p: estimated type-specific probabilities at grid points generated by vectors gridx, gridy.
pvalue: p-value of the Monte Carlo spatial segregation test.
stpvalue: pointwise p-value of the Monte Carlo spatial segregation test.
...: copy of pts, marks, h, opt.

spseg results

an spseg object

Note

Setting h to a unique value may force spseg to skip the selecting bandwidth step, go straight to calculate the type-specific probabilities and then test the spatial segregation with this fixed value of bandwidth.

Author(s)

Barry Rowlingson

Package 'spatialkernel'

Help Index

The Spatialkernel Package

Description

Details

Maintainer

Note

Author(s)

References

See Also

Examples

Signed Area of Polygon

Description

Usage

Arguments

Value

Note

References

See Also

Cross-Validated Log-Likelihood Function Calculate the cross-validated log-likelihood function.

Description

Usage

Arguments

Details

Value

References

See Also

Lansing Woods Trees

Description

Format

Note

Source

References

Level (Contour) Plots with Polygonal Boundary This is a revised version of the base R function filled.contour. It additionally plots a polygonal boundary.

Description

Usage

Arguments

Note

See Also

Inhomogeneous K-function Estimation Estimate the inhomogeneous K function of a non-stationary point pattern.

Description

Usage

Arguments

Details

Value

Note

References

See Also

Kernel Density Estimation of Intensity Function

Description

Usage

Arguments

Details

Value

Note

References

See Also

Monte Carlo Inference of Temporal Changes in Spatial Segregation An approximate Monte Carlo test of temporal changes in a multivariate spatial-temporal point process.

Description

Usage

Arguments

Details

Value

References

See Also

Monte Carlo Test of Spatial Segregation in Multivariate Point Process

Description

Usage

Arguments

Details

Value

References

See Also

Plot Color Level Metre

Description

Usage

Arguments

See Also

Listing Loaded/Installed Package Versions List version numbers of loaded or installed packages.

Description

Level (Contour) Plots with Polygonal Boundary This is a revised version of the base R function `filled.contour`. It additionally plots a polygonal boundary.

Integrated Functions for Spatial Segregation Analysis Spatial segregation analysis to be performed by a single function and presentations by associated `plot` functions.